The process truly couldn't appear easier: simply fill the proprietary bottle with your preferred wine instead of water, and carry out the same steps you would otherwise.
Note that this will infuse your wine with bubbles, but won't improve the taste. True sparkling wine is created through fermentation, so this wine may taste more sharply acidic.
Additionally, know that your SodaStream’s warranty will be void should you attempt to carbonate anything other than water — and doing so can even result in an explosion.